SOLUTION: The base of a solid in the xy-plane is the circle x^2 + y^2 = 16. Cross sections of the solid perpendicular to the y-axis are squares. What is the volume, in cubic units, of the so
Algebra ->
Rational-functions
-> SOLUTION: The base of a solid in the xy-plane is the circle x^2 + y^2 = 16. Cross sections of the solid perpendicular to the y-axis are squares. What is the volume, in cubic units, of the so
Log On
Question 1085534: The base of a solid in the xy-plane is the circle x^2 + y^2 = 16. Cross sections of the solid perpendicular to the y-axis are squares. What is the volume, in cubic units, of the solid? Found 2 solutions by addingup, Edwin McCravy:Answer by addingup(3677) (Show Source):
He's correct for .
He used 25 instead of 16.
The differential of volume is a thin square slab,
(think of a thin square linoleum floor tile) whose
thickness is dx thick. Think of the green slab being
a square (I know it doesn't look like a square, but
pretend it is a square whose edge is on the thin black
strip and imagine it sticking straight up out of the
paper straight up toward you, perpendicular to the
xy-plane, not slanted as it looks like here.)
The length of the edge of the slab is
= =
The vertical height of the slab is the same, since it's square,
and its thickness is dx, so the differential of volume is
or
The slabs go from where x=-4 to +4
So
= =
Finish that by breaking it into two integrals and you'll
end up with .
Edwin
